| Gabor Analysis on Finite Product of Cyclic Groups |
| Received:July 06, 2023 Revised:April 02, 2024 |
| Key Words:
Gabor frame Gabor frame operator modulation translation
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| Author Name | Affiliation | | Jineesh THOMAS | Research Scholar of Mathematics, St.Thomas College Palai, Kottayam, Kerala, 686574, India | | N. M. Madhavan NAMBOOTHIRI | Professor and Principal, Government Arts & Science College Idukki, Kerala, 686013, India | | Ajo JOSE | Research Scholar of Mathematics, St.Thomas College Palai, Kottayam, Kerala, 686574, India |
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| Abstract: |
| We present a complete characterization of Gabor frame operators on finite dimensional Hilbert space $L^2(\Gamma)$, where $\Gamma = \mathbb{Z}_{m_1} \times \mathbb{Z}_{m_2} \times \dots \times \mathbb{Z}_{m_p}$ and $m_1,m_2,\dots,m_p$ are positive integers. The notion of generalized $B$-modulation and generalized $B$-translation is introduced and some significant properties of the generalized pseudo $B$-Gabor like frames are discussed. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.04.011 |
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